# Math Techniques of Calculus I Penn State University Summer Session 2017

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1 Math Techniques of Calculus I Penn State University Summer Session 2017 Instructor: Sergio Zamora Barrera Office: 018 McAllister Bldg sxz38@psu.edu Office phone: Office Hours: M-F 11:00-12:00 Class Time and Location: Willard Bldg 265, M-F, 09:35-10:10. Policy: s sent to me will be replied in less than 48 hours. Course Description: Functions, graphs, derivatives, integrals, techniques of differentiation and integration. Applications to business, economics and social and life sciences. Students may take only one course for credit from MATH 110, 140, 140A, and 140B. Prerequisite: MATH 022 or satisfactory performance on the mathematics proficiency examination. Course Coverage: The goal for the course is to cover the chapters/sections detailed in the tentative class schedule below. Those include most of the contents of chapters 1-6 from the textbook. Textbook: Calculus for Business, Economics, and the Social and Life Sciences, Brief Edition, Tenth Edition. Hoffman, Bradley. McGraw Hill. Tentative Class Schedule (Lectures) Section Date Contents 1.1, /12 Functions and Graphs /13 Linear Functions /14 Functional Models /15 Limits /16 One Sided Limits and Continuity 06/19 Applications

2 Section Date Contents /20 The Derivative /21 Techniques of Derivation /22 Higher Order Derivatives /23 The Chain Rule /26 Marginal Analysis and Approximations /27 Implicit Differentiation 06/28 Applications 06/29 Review Quiz 1 06/30 Chapters 1 and /03 Monotone Functions and Relative Extrema /05 Concavity and Points of Inflection /06 Curve Sketching /07 Optimization and Elasticity of Demand /10 Applied Optimization 07/11 Applications /12 Exponential Functions, Continuous Compounding /13 Logarithmic Functions /14 Differentiation of Exponential and Logarithmic Functions /17 Exponential Models 07/18 Applications 07/19 Review Quiz 2 07/20 Chapters 3 and /21 Indefinite Integral /24 Integration by Substitution /25 Definite Integral and Fundamental Theorem of Calculus /26 Applications /27 Applications /28 Applications /31 Integration by Parts /01 Differential Equations /02 Improper Integrals /03 Numerical Integration 08/04 Applications 08/07 Applications 08/08 Review Final Quiz 08/09 Chapters 5 and 6

3 Learning Objectives: Upon successful completion of Math 110, the student should be able to: 1. Identify polynomial, rational, power, exponential, and logarithmic functions. 2. Calculate the domains of polynomial, rational, power, exponential, and logarithmic functions. 3. Calculate the sums, differences, products, quotients, and compositions of functions. 4. Model cost, revenue, profit, supply, and demand business functions. 5. Calculate equilibrium points within supply/demand markets and interpret the results. 6. Calculate or estimate finite/infinite limits of functions given by formulas, graphs, or tables. 7. Calculate one-sided limits of functions. 8. Determine whether a function given by a graph or formula is continuous at a given point or on a given interval. 9. Determine whether a function given by a graph or formula is differentiable at a given point or on a given interval. 10. Distinguish between average and instantaneous rate of change and interpret the definition of the derivative graphically.

4 11. Determine derivatives of some functions using the definition of derivative of a function. 12. Calculate derivatives of polynomial, rational, power, exponential, and logarithmic functions, and combinations of these functions. 13. Calculate derivatives of implicitly defined functions. 14. Apply the ideas and techniques of derivatives to related rate problems to include basic algebraic/geometric models and cost/average cost, revenue/average revenue, profit/average profit, supply, and demand models. 15. Apply the ideas and techniques of derivatives to perform marginal analysis of basic economics models. 16. Apply the ideas and techniques of derivatives to calculate elasticity of basic economics models. 17. Apply the ideas and techniques of derivatives to determine intervals where a models/graph is: a) Increasing/decreasing. b) Concave up/down. 18. Apply the ideas and techniques of derivatives to determine points in a model/graph that are: a) Relative extrema. b) Absolute extrema.

5 c) Critical Values. d) Points of Inflection. 19. Identify vertical and horizontal asymptotic. 20. Apply the ideas and techniques of derivatives to graphing or recognizing the graphs of functions. 21. Apply the ideas and techniques of derivatives to optimization problems to include basic algebraic/geometric models and cost, revenue, profit, supply, and demand models. 22. Apply the ideas and techniques of derivatives to solve: a) Compound interest. b) Continuous interest. c) Effective interest rate. d) Present value business models. 23. Determine the point-of-diminishing returns for a model/function. 24. Calculate the derivatives of functions using logarithmic differentiation. 25. Calculate the Riemann sum for a given function, partition and collection of evaluation points. 26. Describe a definite integral as the limit of a Riemann sum.

6 27. Determine anti-derivatives of basic algebraic functions. 28. Calculate values of definite integrals using anti-derivatives and areas. 29. Apply concepts of integration to solving basic business model applications. 30. Apply substitution and integration by parts techniques to integrate basic functions. 31. Apply the ideas of definite integrals to solve problems of areas. 32. Calculate the average value of business models using the definite integral. 33. Apply the ideas and techniques of the definite integral to evaluate: a) Consumer/producer surplus. b) Future/present value of income streams. c) Future/present value of annuities business models. 34. Evaluate improper integrals and apply the ideas and techniques to evaluate perpetuities. Grading policy: Grades will be assigned on the basis of 1300 points distributed as follows: Homework 600 Quiz Quiz Final Quiz 300 Total 1300

8 Academic Misconduct: I this course academic misconduct includes, but is not limited to: 1. Copying the work of another student, on an exam, quiz or assignment. 2. Passing off the work of another individual as your own. 3. Using non-approved devices or aids on exams, quizzes or assignments. 4. Having unauthorized possession of exams or quizzes. 5. Engaging in deception in order to extend or reschedule an exam, quiz or assignment. 6. Facilitating acts of academic misconduct by others. When Academic Misconduct is Suspected: If a student is suspected of academic misconduct, the instructor s duties are to: 1. Confidentially inform the student of the allegation. 2. Enter the charge and recommended sanctions on an Eberly College or Science Academic Integrity form. 3. Ask the student to meet in order to review the form and discuss the charge and sanctions. The student can choose to accept or contest the allegation at this point. Note that a student s refusal to meet with the instructor or respond to the charges within a reasonable period of time is construed as acceptance of the allegation and proposed sanctions.

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